SSLC (English Medium) इयत्ता १० - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ² = 2PR² + QR² 

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?

What is the slope of a line whose inclination with positive direction of x-axis is 90°

What is the slope of a line whose inclination with positive direction of x-axis is 0°

What is the inclination of a line whose slope is 0

What is the inclination of a line whose slope is 1

Find the slope of a line joining the points

`(5, sqrt(5))` with the origin

Find the slope of a line joining the points

(sin θ, – cos θ) and (– sin θ, cos θ)

What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4, 2) and (–6, 4).

Show that the given points are collinear: (– 3, – 4), (7, 2) and (12, 5)

If the three points (3, – 1), (a, 3) and (1, – 3) are collinear, find the value of a

The line through the points (– 2, a) and (9, 3) has slope `-1/2` Find the value of a.

The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem

A(1, – 4), B(2, – 3) and C(4, – 7)

Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem.

L(0, 5), M(9, 12) and N(3, 14)

Show that the given points form a parallelogram:

A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5)

If the points A(2, 2), B(– 2, – 3), C(1, – 3) and D(x, y) form a parallelogram then find the value of x and y.

Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7). Show that ABCD is a trapezium.

A quadrilateral has vertices at A(– 4, – 2), B(5, – 1), C(6, 5) and D(– 7, 6). Show that the mid-points of its sides form a parallelogram.

The slope of the line joining (12, 3), (4, a) is `1/8`. The value of ‘a’ is